1. Field of the Invention
The present invention relates to the process of semiconductor manufacturing. More specifically, the present invention relates to a method and an apparatus for accurately modeling an apodization effect or lens transmission behavior in an optical lithography system which is used in semiconductor manufacturing.
2. Related Art
Semiconductor manufacturing technologies typically include a number of processes which involve complex physical and chemical interactions. Since it is almost impossible to find exact formulae to predict the behavior of these complex interactions, developers typically use process models which are fit to empirical data to predict the behavior of these processes. A process model can be used in a number of applications during the design of a semiconductor chip.
For example, in a technique which is referred to as “Optical Proximity Correction” (OPC), a process model is used to make corrections to a semiconductor chip layout to compensate for undesirable effects of semiconductor manufacturing processes. An OPC model is typically composed of a physical optical model and an empirical process model. An OPC simulation engine uses the OPC model to iteratively evaluate and modify edge segments in the mask layout. In doing so, the OPC simulation engine computes the correct mask patterns which produce physical patterns on wafer that closely match a desired design layout. Note that the effectiveness of the corrected mask patterns is typically limited by the accuracy of the OPC model.
Currently, semiconductor manufacturers are using lithography systems with numerical apertures (NA) near 1 or even larger than 1 (referred to as “hyper-NA”), while continuously pushing ever larger NAs to achieve increasingly smaller critical dimensions (CDs). Existing OPC models are capable of modeling many high-NA related optical effects such as: thin-film energy coupling, vector diffraction, polarization illumination, and immersion imaging. Unfortunately, none of these existing OPC models can accurately predict pupil apodization effects in such lithography systems.
An apodization effect is a lens optical transmission attenuation effect which is caused by imperfections in optical components (e.g., absorption, size and shape of the lens pupil). Apodization effects can cause frequency-dependent amplitude or intensity attenuation especially in high-spatial-frequency region in the lens pupil. Note that the high-spatial-frequency components are typically important to the image formation or printing of design features with small critical dimensions. Hence, the apodization effects are becoming a limiting factor in the lithography process as feature sizes continue to shrink.
Existing OPC modeling techniques approximate the apodization effect by using an ideal Gaussian model with a single tunable parameter, i.e., Gaussian Sigma (σ). However, this single parameter ideal Gaussian model does not suffice to predict the measured transmission attenuation for the actual apodization effect. More specifically, no single σ value can be found to reasonably fit this ideal Gaussian model to match the entire spatial frequency spectrum of the transmission data. For example, it has been observed that an ideal Gaussian apodization model can cause greater than 5 nm or even 15 nm CD errors when it is used in a 65 nm-node benchmark test.
Furthermore, an ideal Gaussian apodization model is commonly regressed simultaneously with other parameters from non-optical models to calibrate a multi-parameter OPC model. However, this multi-dimensional optimization technique typically changes the value of the apodization parameter σ. Additionally, because the ideal Gaussian model is inherently inaccurate, this multi-variable regression approach can cause additional OPC model inaccuracy or distortion because other non-optical OPC model components, such as resist model or etch model components, can be unintentionally distorted to compensate for the inaccuracy in the OPC optical model. Note that such a divergence of empirical resist or etch model from the real physical behavior is usually extremely difficult to detect based on a limited training data set, and can pose a serious risk to overall OPC model stability and accuracy.
Hence, what is needed is a method and an apparatus to accurately model an apodization effect in an optical lithography system without the above described problems.